This paper extends and generalizes the subspace analysis of the
Hopfield Network presented in our earlier work [IEEE trans. NN. 6/90].
In [IEEE trans. NN. 6/90] it was shown that the ability of the
Hopfield Network to confine a vector within a particular subspace was
essential to the network's ability to reach valid solutions to the
Travelling Salesman problem. Through the use of Kronecker (Tensor)
products, this paper shows how an analogous subspace can be
constructed for a much larger class of combinatorial optimization
problems. By using the form of this subspace as the basis for
determining the elements of the network connection matrix, convergence
to a valid solution can be guaranteed. Further, the quality of the
final solution is significantly improved. This is confirmed by
benchmark experiments using 30 and 50 city Travelling Salesman
problems as an illustrative example. These indicate that the network
can reliably and efficiently achieve solutions within 2\% of the
global optimum.

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